A perfect linear relationship yields a correlation coefficient of
+1 (or -1 for a negative relationship) and no linear relationship
yields a correlation coefficient of 0.

Partial correlation is the correlation between two variables
after removing the effect of one or more additional variables. This
command is specifcally for the the case of one additional variable.
In this case, the partial correlation can be computed based on
standard correlations between the three variables as follows:

As with the standard correlation coefficient, a value of +1 indicates
a perfect positive linear relationship, a value of -1 indicates a
perfect negative linear relationship, and a value of 0 indicates no
linear relationship.

It may be of interest to determine if the partial correlation
is significantly different than 0. The CDF value for this
test is

CDF = FCDF(VAL,1,N-3)

where FCDF is the F cumulative
distribution function with 1 and N - 3 degrees of freedom
(N is the number of observations) and
VAL = ABS((N-3)*R**2/(1 - R**2)) with R denoting the
computed partial correlation. The pvalue is 1 - CDF.

Syntax 1:

LET <par> = PARTIAL CORRELATION <y1> <y2>
<y3>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
<y3> is the third response variable;
<par> is a parameter where the computed partial
correlation is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Syntax 2:

LET <par> = PARTIAL CORRELATION ABSOLUTE VALUE
<y1> <y2> <y3>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
<y3> is the third response variable;
<par> is a parameter where the computed partial
correlation absolute value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the absolute value of the partial correlation
coefficient. This is typically used in screening applications where
there is an interest in identifying high magnitude correlations
regardless of the direction of the correlation.

Syntax 3:

LET <par> = PARTIAL CORRELATION PVALUE
<y1> <y2> <y3>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
<y3> is the third response variable;
<par> is a parameter where the computed partial
correlation pvalue is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the pvalue (described above) of the partial
correlation.

Syntax 4:

LET <par> = PARTIAL CORRELATION CDF
<y1> <y2> <y3>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
<y3> is the third response variable;
<par> is a parameter where the computed partial
correlation cdf is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the cdf (described above) of the partial
correlation.